Question 334674
A plane flying the 3020-mile trip from City A to City B has a 60 mph tailwind.
 The flights point of no return is the point at which the flight time required
 to return to City A is the same as the time required to continue to City B.
 If the speed of the plane in still air is 430 mph, how far from City A is the point of no return? 
:
Not sure why you need two variables here.
:
>>>>>>>>>>>>60 mph wind>>>>>>>>>>>>>>>
A-------------p-----------------------B
|----------------3020 mi--------------|
:
Let p = the distance from A to the point of no return
then
(3020-p) = the distance from B to the point of no return
:
430 + 60 = 490 mph; effective speed with the wind (continue to B)
and
430 - 60 = 370 mph; effective speed against the wind (return to A)
:
Write a time equation, Time = dist/speed
:
Time to return to A = Time to continue to B
{{{p/370}}} = {{{(3020-p)/490}}}
Cross multiply
490p = 370(3020-p)
490p = 1117400 - 370p
490p + 370p = 1117400
860p = 1117400
p = {{{1117400/860}}}
p = 1299.3 mi from A is the point of no return
:
:
See if this is true, find the time from p to A & B
dist to B = 3020 - 1299.3 = 1720.7
1299.3/370 = 3.51 hrs back to A
1720.7/490 = 3.51 hrs to B